So as the consort of an enthroned monarch, her rank in the British royal court would have risen. I'm not sure about her exact position, however -- and whether, in particular, she outranked her sisters-in-law even when not in the presence of her husband.
Even before the Duke of Edinburgh's accession to his uncle's throne, however, the family had been living for some time in Germany -- precisely in preparation for the event. He had to serve a period of apprenticeship in being groomed as heir; ditto for his only son, Prince Alfred. So the duchess was spared the ordeal of having to put up with the *offensive* presence of her sisters-in-law, the indignity of having to yield precedence to them at the British royal court.
I don't know whether, in Coburg, she was allowed to style herself as Imperial Highness: in Great Britain, she was required herself to style herself Royal first, Imperial second. But perhaps in Germany, there was more respect for a woman's birth rank. The Grand Duchess Maria Alexandrovna of Russia had, in fact, been born to the imperial rank, even though she was not at the time (1853) an emperor's daughter (she was nonetheless a granddaughter through son of Czar Nicholas I).